efficient va hedging instruments for target volatility ... · global markets . deutsche bank ....

Efficient VA Hedging Instruments for Target Volatility Portfolios

Jon Spiegel

Deutsche Bank

Equity Structuring | Global Investment Solutions | Global Markets

Efficient VA Hedging Instruments For Target Volatility Portfolios Jon Spiegel, Director | 212-250-6054 EBIG Conference - Chicago November 14, 2016 - 13:30 to 15:00 hours

For Institutional Investors Only – Not for Retail Distribution

Global Markets Deutsche Bank

Disclaimer (1/2)

11/12/2016 9:52:13 AM 2010 DB Blue template

1

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Efficient VA Hedging Instruments For Target Volatility Portfolios

Agenda


3

1 • Target Volatility Risk Properties

2 • Target Volatility Puts vs. Vanillas

3 • Other Tactical Hedging Instruments


Target Volatility Risk Properties

Introduction


4

(1) Source: DB Equity Derivatives Research

Over the past five years, the AUM of VA managed volatility funds has grown to over $200bn1

Target volatility strategies are likely to exhibit long-term volatilities close to their targets, neutralizing the vega exposure of VA guarantees

However instantaneous equity risk scenarios still show significant crash-risk. Hedge with vanillas?



Example: S&P 500 Risk Control Indices


5

Source: Bloomberg Finance L.P. and DB Structuring

0

50

100

150

200

250

300

SPXT10UT SPXT15UT SPXT



Realized Volatility (1yr)


6


0%

5%

10%

15%

20%

25%

30%

35%

40%

45%

50% SPXT10UT SPXT15UT SPXT SPXT10UT-Avg SPXT15UT-Avg SPXT-Avg



Realized Skew: Realized Volatility vs. Returns (Semi-annual, Dec ’99 – Jun ‘16)


7

y = -0.02x + 0.15

y = -0.11x + 0.10

y = -0.51x + 0.19

0%

10%

20%

30%

40%

50%

60%

-30% -20% -10% 0% 10% 20% 30%

SPXT10UT

SPXT15UT

SPXT


6m Return

6m R

ealiz

ed V

ol



Historical SPX Implied Volatility vs. Subsequent Realized (12/31/1999 – 5/10/2016)


8

Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research

0%

10%

20%

30%

40%

50%

60%

70% SPX 6m ATM Implied Vol

SPX 6m 90% Implied Vol

Subsequent 6m Realized


-40%

-30%

-20%

-10%

0%

10%

20%

30% ATM Implied - Realized

90% Implied - Realized


SPX 6m Implied vs. Subsequent Realized Spread (12/31/1999 – 5/10/2016)


9


Strike Avg Since Dec ’99

Avg Since Jan ’09

90% 5.58% 8.07%

100% 1.80% 3.75%


Target Volatility Puts vs. Vanillas

Introduction


10

Intuitively it should be more efficient to hedge liabilities linked to target volatility funds using puts on target volatility indices to avoid overpaying for implied volatility and skew

We compare the performance of hypothetical target volatility puts with the performance of comparable listed options

Caveats: (1) The target vol index is a systematic proxy for portfolios which generally contain discretionary funds with diverse mandates (2) Target volatility puts are not widely traded, so pricing is hypothetical



Comparable Instruments Methodology


11

We compare the PL from buying puts on target volatility indices with the PL from buying comparable vanilla puts, for each trade date

Comparing target volatility puts with vanilla equity puts requires careful consideration as the vanilla equity put embedded in a TV put has changing notional and strike over the life of the trade

We adjust the vanilla strike and notional to have equivalent intrinsic value on trade date for all equity scenarios (“equal crash protection”)

Dynamic Adjustment: Compare TV put to scaled vanilla put adjusted using most recent TV Participation Static Adjustment: Compare TV put to scaled vanilla put using fixed long-term average TV Participation



Comparable Instruments Adjustment


12

Target Volatility

Index Cash

Allocation

Strike (e.g. 95%) Notional Adjustment

Strike Adjustment

%ionParticipatTVNotionalTVNotionalVanilla

%

%1%100

ionParticipatTV

StrikeTVStrikeVanilla

Equity Allocation

(not to scale)



Back-test methodology for TV 10% 6m 95% Put, Dynamically Adjusted


13

• For each trading day, locate SPX listed expiration closest to 6 months Select Listed Expiration

• For selected expiration, locate strike closest to participation-adjusted TV equivalent

• Example: 70% participation 1-.05/.7 = 92.85% Select Scaled Vanilla Strike

• Adjust TV tenor and strike slightly to correspond with listed option used for scaled vanilla Adjust TV Tenor and Strike

• 10% TV 6m 95% put BS: 12.51 vol, fwd = libor flat • 10% TV 12m 90% put BS: 12.51 vol, fwd = libor flat • Scaled Vanilla Listed mid-market

Price TV and Vanilla Puts

(1) Indicative and hypothetical


0%

2%

4%

6% Target Vol Price Target Vol Payoff

Target Volatility Puts vs. Vanillas SPXT10UT 6m 95%; Dynamic Adjustment

Average Price and Payoff by Trade Date Year


14


0%

2%

4%

6% Scaled Vanilla Price Scaled Vanilla Payoff



PL by Trade Date (Jan ’00 – Oct ’161)


15

(1) Assuming that options unexpired as of Nov 11, 2016 expire OTM Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research

-15%

-10%

-5%

0%

5%

10%

15%

Trade Date

Scaled Vanilla PL Target Vol PL TV - Scaled Vanilla



PL by Trade Date (Since 20091)


16

(1) Assuming that options unexpired as of Nov 11, 2016 expire OTM Source: Bloomberg Finance L.P., DB Structuring and DB Equity Derivatives Research

-5%

-4%

-3%

-2%

-1%

0%

1%

2%

3%

4%

5%

Trade Date

Scaled Vanilla PL Target Vol PL TV - Scaled Vanilla



Target Vol Behavior in Different Sell-Offs


17


Source: DB Structuring, Bloomberg

0% 20% 40% 60% 80% 100%

0%

50%

100%

Jun-15 Jul-15 Aug-15 Sep-15 Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Participation (RHS) SPXT10UT SPXT

0% 20% 40% 60% 80% 100%

0%

50%

100%

Jun-07 Sep-07 Dec-07 Mar-08 Jun-08 Sep-08 Dec-08 Mar-09 Jun-09

Participation (RHS) SPXT10UT SPXT


-0.4%

0.7%

-0.8%

0.3% 0.9% 0.7% 0.7% 0.3%

-3.6%

0.0%

0.6% 1.0% 0.8% 0.7% 0.9% 0.8% 0.6%

-5%

0%

5%

TV - Scaled Vanilla PL

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

SPX Return SPXT10UT Return


Target Vol Put vs. Scaled Vanilla PL, Average by Trade Year


18


Since 2000 0.25% (0.50% p.a.)

Since 2009 0.67% (1.34% p.a.)


-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%


-0.3%

0.5%

-0.5%

0.5% 1.5% 1.2% 1.1%

-0.8% -3.8%

0.1% 1.1% 1.0% 1.6% 1.5% 1.7% 1.0%

-5%

0%

5%





19


Since 2000 0.47% p.a.

Since 2009 1.15% p.a.



Comparable Instruments Methodology


20


We assume that the liability’s equity exposure matches the proxy index. But comparing to the vanilla, does a daily dynamic participation adjustment fairly capture equal crash risk?

Hedging with vanillas, as participation increases (decreases) would need to buy (sell) puts to hedge crash risk of target vol liability. IE, buy when vol is falling, sell when vol is rising

In another comparison we adjust each vanilla put strike and notional using the same long-term participation of 67%

0% 20% 40% 60% 80%

100% 120% 140% 160%

SPXT10UT Participation Average = 67%


-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%


-0.7% -0.1% -0.4%

0.8% 0.2%

-0.1% -0.1% -0.3%

-5.3%

2.4% 1.3% 2.1% 0.7%

0.0% -0.1%

1.1% 0.4%

-10.0%

-5.0%

0.0%

5.0%


Target Volatility Puts vs. Vanillas Back-tested PL Comparison – 6m 95% Static (67% Participation)



21


Since 2000 0.14% (0.28% p.a.)

Since 2010 1.0% (2.0% p.a.)



Dynamic vs. Static Hedging with Vanillas


22


0%

20%

40%

60%

80%

100%

120%

-6%

-4%

-2%

0%

2%

4%

6%

8% Participation (RHS) Scaled Vanilla PL, Dynamic Scaled Vanilla PL, Static

Dynamic buys more, puts expire OTM

Dynamic buys less, puts expire ITM

Dynamic buys less, puts expire OTM


Other Tactical Hedging Instruments


23

• Finance tail risk protection by selling ATM gamma 1x2 Put Spread

• Monetize skew to buy cheap vega, plus 1-day gap protection

Conditional Up-Variance Swap

• Monetize vol and skew with limited risk Variance KO Put


Delta-Hedged 1x2 Put Spread


24

Using vanilla options, VA hedgers can set up a position that provides:

• Positive carry • Long skew, Long convexity, Deep tail risk protection

The strategy entails:

• Selling an ATM or near-ATM put • Buying 2 OTM puts • Delta hedging

In return for the above benefits, seller is exposed to high implied or realized volatility without a significant selloff in spot

Applicability: Target vol liabilities may incur less daily delta hedging than traditional VA and would be better positioned to sell local gamma


Delta-Hedged 1x2 Put Spread SPX 6m, Delta-based strikes

Indicative PL Back-test: Sell $1/6 notional every month


25


0

500

1,000

1,500

2,000

2,500

-2%

0%

2%

4%

6%

8%

10%

12%

14%

50d/5d 50d/10d SPX (RHS)



Strikes Back-test


26


0

500

1000

1500

2000

2500 SPX 50d Avg Strike 5d Avg Strike 10d Avg Strike



Gamma Back-test


27


0

500

1,000

1,500

2,000

2,500

-1.0%

-0.8%

-0.6%

-0.4%

-0.2%

0.0%

0.2%

0.4%

0.6%




Vega Back-test


28


0

500

1,000

1,500

2,000

2,500

-0.20% -0.15% -0.10% -0.05% 0.00% 0.05% 0.10% 0.15% 0.20% 0.25%



ind(Pt-1) equals 0 if spot at t – 1 is above barrier, otherwise equal to 1

N is expected number of trading days from Trade to Expiration

“Conditional Up-Variance Swaps” only accrue variance if the spot price is above a barrier.

Applicability: Use ITM (downside) barrier; Provide 1-day gap protection as barrier is observed t-1; Best for portfolios requiring some long vega exposure



29

Nt

t

Nt

t

ind

ind

11t

11t

2

1-t

t

)P(

)P(P

Pln252

zedUpVarReali

zed)UpVarReali- ke(UpVarStriatioOccurenceRNotionalPayoff

N

ind

Nt

t

1

1t )P(

atioOccurenceR



Given steep skew, up-variance strikes are lower than regular variance


30

(1) Hypothetical back-test

Source: DB Structuring

76% 78% 80% 82% 84% 86% 88% 90% 92% 94%

0%

10%

20%

30%

40%

50%

60%

70%

Indicative SPX 6m Up-Var Strike Indicative SPX 6m Var Strike Barrier = 25% delta put strike (RHS)

Average Spread = 3.81

Trade Date



Realized Conditional Variance and Occurrence Ratio


31

Source: Bloomberg Finance, LP and DB Structuring

0%

20%

40%

60%

80%

100%

120%

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%

Realized 6m Var

Realized 6m Up-Var

Occurrence Ratio (RHS)

Trade Date



Except for Trades done in 2008, Up-Var generally would have outperformed regular Var


32

(1) Hypothetical back-test


Trade Date

-20% -10%

0% 10% 20% 30% 40% 50% 60% 70%

6m Var PL 6m Up-Var PL (Equal Var Notional)

Average Spread = .441 vols Since 2009 = 2.951 vols


0.00

0.20

0.40

0.60

0.80

1.00

1.20

40% 60% 80% 100% 120% 140% 160% 180%

Regular Var Vega Upvar Vega


Vega scenarios (6m, 92% barrier)


33


Spot % of Initial


A Variance Knock-Out Put pays zero if the realized variance surpasses a “budget” during the life of the trade. Otherwise it pays the same as a vanilla.

Applicability: Typically traded by hedge funds. Structure is short-vega and skew, with limited liability. Target volatility hedgers may be positioned to sell vega and skew opportunistically

Variance Knock-Out Put


34

Example: Underlying: SPX Tenor: 6m Strike: ATM Spot Variance Budget: (Implied Variance)^2 * 0.5 Implied Variance: 0.19 Indicative Cost: 1.3% (72% discount to Vanilla) Vanilla 6m ATM Put: 4.6%

2t

1i 1i

i

S

SlntVariance Realized

PX

PX



Implied skew and convexity premia cause the VKO to price the survival rate lower than statistically observed


35

(1) Hypothetically back-tested

Source: Bloomberg Finance L.P and DB Structuring

Most negative SPX Returns Avg SPX Return Survival Rate

Avg VKO Px/ Vanilla Px1

0% to 5% -36.27% 0.0% 28.5%

5% to 10% -15.89% 22.9% 28.4%

10% to 15% -7.89% 54.3% 28.4%

15% to 20% -4.42% 65.7% 28.8%

20% to 25% -2.35% 46.2% 29.1%

25% to 30% -0.19% 81.9% 29.5%

30% to 35% 1.78% 89.5% 35.9%

35% to 40% 2.93% 94.3% 33.2%

Quantile Analysis: SPX 6m ATM VKO; barrier = 6m SPX implied variance on trade date Trade Dates Jan ’08 to Apr ‘16



Vega Evolution: SPX 6m ATM VKO (19.4% budget) Back-Tested from 10/30/2015


36

Source: Bloomberg Finance L.P and DB Structuring

1650 1700 1750 1800 1850 1900 1950 2000 2050 2100 2150

0.0%

0.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Mar-16

VKO Price

SPX (Right)

15%

17%

19%

21%

23%

-0.6%

-0.5%

-0.4%

-0.3%

-0.2%

-0.1%

0.0%

0.1%

0.2%

Oct-15 Nov-15 Dec-15 Jan-16 Feb-16 Mar-16

VKO Vega Vol MTM of Varswap (Right)


Final Thoughts


37

Target volatility strategies exhibit less skew as well as more predictable volatility than pure equity. Hedging strategies should benefit from both of these characteristics.

Buying puts on TV Indices may provide crash protection with less risk premium cost.

“Light Exotics” such as Conditional Variance and VKO’s can monetize expensive skew.

Ongoing work: -- Assessing tracking error of VA Portfolios vs. TV Indices. Designing custom

benchmarks where appropriate -- Price discovery for Target Volatility Puts -- Portfolio diversification from trading combinations of these instruments

efficient va hedging instruments for target volatility ... · global markets . deutsche bank ....

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